Ever since humans began to communicate through pictures, they faced a dilemma of how to accurately represent the three-dimensional world they lived in. Sculpture was used to successfully depict three-dimensional objects, but was not adequate to communicate spatial relationships between objects and within environments. To do this, early humans attempted to “flatten” what they saw around them onto two-dimensional, vertical planes (e.g. paintings, drawings, tapestries, etc.). Scenes where a person stood upright, surrounded by trees, were rendered relatively successfully on a vertical plane. But how could they represent a landscape, where the ground extended out horizontally from where the artist was standing, as far as the eye could see?
The answer is three dimensional illusions. The two dimensional pictures must provide a numbers of cues of the third dimension to the brain to create the illusion of three dimensional images. This effect of third dimension cues can be realistically achievable due to the fact that the brain is quite accustomed to it. The three dimensional real world is always and already converted into two dimensional (e.g. height and width) projected image at the retina, a concave surface at the back of the eye. And from this two dimensional image, the brain, through experience and perception, generates the depth information to form the three dimension visual image from two types of depth cues: monocular (one eye perception) and binocular (two eye perception). In general, binocular depth cues are innate and biological while monocular depth cues are learned and environmental.
The major binocular depth cues are convergence and retinal disparity. The brain measures the amount of convergence of the eyes to provide a rough estimate of the distance since the angle between the line of sight of each eye is larger when an object is closer. The disparity of the retinal images due to the separation of the two eyes is used to create the perception of depth. The effect is called stereoscopy where each eye receives a slightly different view of a scene, and the brain fuses them together using these differences to determine the ratio of distances between nearby objects.
Binocular cues are very powerful perception of depth. However, there are also depth cues with only one eye, called monocular depth cues, to create an impression of depth on a flat image. The major monocular cues are: overlapping, relative size, linear perspective and light and shadow. When an object is viewed partially covered, this pattern of blocking is used as a cue to determine that the object is farther away. When two objects known to be the same size and one appears smaller than the other, this pattern of relative size is used as a cue to assume that the smaller object is farther away. The cue of relative size also provides the basis for the cue of linear perspective where the farther away the lines are from the observer, the closer together they will appear since parallel lines in a perspective image appear to converge towards a single point. The light falling on an object from a certain angle could provide the cue for the form and depth of an object. The distribution of light and shadow on a objects is a powerful monocular cue for depth provided by the biologically correct assumption that light comes from above.
Perspective drawing, together with relative size, is most often used to achieve the illusion of three dimension depth and spatial relationships on a flat (two dimension) surface, such as paper or canvas. Through perspective, three dimension objects are depicted on a two dimension plane, but “trick” the eye into appearing to be in three dimension space. The first theoretical treatise for constructing perspective, Depictura, was published in the early 1400's by the architect, Leone Battista Alberti. Since the introduction of his book, the details behind “general” perspective have been very well documented. However, the fact that there are a number of other types of perspectives is not well known. Some examples are military, cavalier, isometric, and dimetric, as shown at the top of FIG. 1.
Of special interest is the most common type of perspective, called central perspective, shown at the bottom left of FIG. 1. Central perspective, also called one-point perspective, is the simplest kind of “genuine” perspective construction, and is often taught in art and drafting classes for beginners. FIG. 2 further illustrates central perspective. Using central perspective, the chess board and chess pieces look like three dimension objects, even though they are drawn on a two dimensional flat piece of paper. Central perspective has a central vanishing point, and rectangular objects are placed so their front sides are parallel to the picture plane. The depth of the objects is perpendicular to the picture plane. All parallel receding edges run towards a central vanishing point. The viewer looks towards this vanishing point with a straight view. When an architect or artist creates a drawing using central perspective, they must use a single-eye view. That is, the artist creating the drawing captures the image by looking through only one eye, which is perpendicular to the drawing surface.
The vast majority of images, including central perspective images, are displayed, viewed and captured in a plane perpendicular to the line of vision. Viewing the images at angle different from 90° would result in image distortion, meaning a square would be seen as a rectangle when the viewing surface is not perpendicular to the line of vision. However, there is a little known class of images that we called it “horizontal perspective” where the image appears distorted when viewing head on, but displaying a three dimensional illusion when viewing from the correct viewing position. In horizontal perspective, the angle between the viewing surface and the line of vision is preferrably 45° but can be almost any angle, and the viewing surface is perferrably horizontal (wherein the name “horizontal perspective”), but it can be any surface, as long as the line of vision forming a not-perpendicular angle to it.
Horizontal perspective images offer realistic three dimensional illusion, but are little known primarily due to the narrow viewing location (the viewer's eyepoint has to be coincide precisely with the image projection eyepoint), and the complexity involving in projecting the two dimensional image or the three dimension model into the horizontal perspective image.
The generation of horizontal perspective images require considerably more expertise to create than conventional perpendicular images. The conventional perpendicular images can be produced directly from the viewer or camera point. One need simply open one's eyes or point the camera in any direction to obtain the images. Further, with much experience in viewing three dimensional depth cues from perpendicular images, viewers can tolerate significant amount of distortion generated by the deviations from the camera point. In contrast, the creation of a horizontal perspective image does require much manipulation. Conventional camera, by projecting the image into the plane perpendicular to the line of sight, would not produce a horizontal perspective image. Making a horizontal drawing requires much effort and very time consuming. Further, since human has limited experience with horizontal perspective images, the viewer's eye must be positioned precisely where the projection eyepoint point is to avoid image distortion. And therefore horizontal perspective, with its difficulties, has received little attention.